Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shell

摘要

AbstractThe purpose of this paper is to study bifurcation points of the equationT(v) =L(λ,v) +M(λ,v), (λ,v) ϵ Λ ×Din Banach spaces, where for any fixed λ ϵ Λ,T,L(λ,·) are linear mappings andM(λ,·) is a nonlinear mapping of higher order,M(λ,0) = 0 for all λ ϵ Λ. We assume thatλis a characteristic value of the pair (T,L) such that the mappingT–L(λ,·) is Fredholm with nullitypand indexs,p>s⩾ 0. We shall find some sufficient conditions to show that (λ,0) is a bifurcation point of the above equation. The results obtained will be used to consider bifurcation points of the axisymmetric buckling of a thin spherical shell subjected to a uniform compressive force consisting of a pair of coupled non‐linear ordinary differential